Geometry of ordinary equations. Symmetries. Applications of
symmetries to solving ODEs. Lie-Bianchi theorem on integration
of ODEs by quadratures.
Contact geometry and the theory of first-order equations.
Relation to symplectic geometry and Hamiltonian mechanics.
Finite jets of submanifolds. Cartan distribution. Integral manifolds.
Differential equations as geometric objects. Theory of symmetries.
Application of symmetries (invariant solutions, reproduction
of solutions, factorization). Examples. External and internal
geometry of equations.
Infinite jets. Algebraic formalism. Prolongation of differential
equations. Higher symmetries and their computation. Examples.
Computer methods for finding symmetries.
Conservation laws and their computation. Noether theorem.
Hamiltonian structures. Examples.
Coverings over differential equations and nonlocal symmetries.
Questions and suggestions should go to Jet Nestruev,
jet @ diffiety.ac.ru.